TY - JOUR

T1 - Estimating activity cycles with probabilistic methods I. Bayesian Generalised Lomb-Scargle Periodogram with Trend

AU - Olspert, N.

AU - Pelt, J.

AU - Käpylä, M. J.

AU - Lehtinen, J. J.

PY - 2018/7

Y1 - 2018/7

N2 - Period estimation is one of the central topics in astronomical time
series analysis, where data is often unevenly sampled. Especially
challenging are studies of stellar magnetic cycles, as there the periods
looked for are of the order of the same length than the datasets
themselves. The datasets often contain trends, the origin of which is
either a real long-term cycle or an instrumental effect, but these
effects cannot be reliably separated, while they can lead to erroneous
period determinations if not properly handled. In this study we aim at
developing a method that can handle the trends properly, and by
performing extensive set of testing, we show that this is the optimal
procedure when contrasted with methods that do not include the trend
directly to the model. The effect of the noise model on the results is
also investigated. We introduce a Bayesian Generalised Lomb-Scargle
Periodogram with Trend (BGLST), which is a probabilistic linear
regression model using Gaussian priors for the coefficients and uniform
prior for the frequency parameter. We show, using synthetic data, that
when there is no prior information on whether and to what extent the
true model of the data contains a linear trend, the introduced BGLST
method is preferable to the methods which either detrend the data or
leave the data untrended before fitting the periodic model. Whether to
use different from constant noise model depends on the density of the
data sampling as well as on the true noise model of the process.

AB - Period estimation is one of the central topics in astronomical time
series analysis, where data is often unevenly sampled. Especially
challenging are studies of stellar magnetic cycles, as there the periods
looked for are of the order of the same length than the datasets
themselves. The datasets often contain trends, the origin of which is
either a real long-term cycle or an instrumental effect, but these
effects cannot be reliably separated, while they can lead to erroneous
period determinations if not properly handled. In this study we aim at
developing a method that can handle the trends properly, and by
performing extensive set of testing, we show that this is the optimal
procedure when contrasted with methods that do not include the trend
directly to the model. The effect of the noise model on the results is
also investigated. We introduce a Bayesian Generalised Lomb-Scargle
Periodogram with Trend (BGLST), which is a probabilistic linear
regression model using Gaussian priors for the coefficients and uniform
prior for the frequency parameter. We show, using synthetic data, that
when there is no prior information on whether and to what extent the
true model of the data contains a linear trend, the introduced BGLST
method is preferable to the methods which either detrend the data or
leave the data untrended before fitting the periodic model. Whether to
use different from constant noise model depends on the density of the
data sampling as well as on the true noise model of the process.

KW - Astrophysics - Solar and Stellar Astrophysics

KW - Astrophysics - Instrumentation and Methods for Astrophysics

KW - Statistics - Applications

KW - Statistics - Machine Learning

U2 - 10.1051/0004-6361/201732524

DO - 10.1051/0004-6361/201732524

M3 - Article

VL - 615

SP - 1

EP - 13

JO - Astronomy & Astrophysics

JF - Astronomy & Astrophysics

SN - 0004-6361

M1 - A111

ER -